Minimal coexistence configurations for multispecies systems

TL;DR

This paper investigates the behavior of multispecies Lotka-Volterra systems in complex domains, showing that as competition intensifies, species segregate spatially and the system reaches a stable coexistence configuration.

Contribution

It establishes the existence of minimal coexistence configurations in strongly competing multispecies systems within dumbbell-like domains, extending understanding of spatial segregation and stability.

Findings

Species segregate spatially as competition increases

Limit configurations are local minimizers of free energy

Results apply to complex domain geometries

Abstract

We deal with strongly competing multispecies systems of Lotka-Volterra type with homogeneous Neumann boundary conditions in dumbbell-like domains. Under suitable non-degeneracy assumptions, we show that, as the competition rate grows indefinitely, the system reaches a state of coexistence of all the species in spatial segregation. Furthermore, the limit configuration is a local minimizer for the associated free energy.